Some modest Yahtzee goals

If the probability of getting at least one pair of matching dice when rolling five 6-sided dice is \(\frac{a}{b}\), where \(a\) and \(b\) are positive co-prime integers, then what is \(a+b\)?

Note: Three-of-a-kind, four-of-a-kind, full house, yahtzee, or two pairs would all count as "at least one pair of matching dice." However, a straight (\(\{1,2,3,4,5\}\) or \(\{2,3,4,5,6\}\)) or a small straight would not count.


Check out The anti-Yahtzee first to make finding the solution to this problem trivial.

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